The sum of the first 100 natural numbers is exactly 5050.
The question asks for the sum of the natural numbers from 1 to 100. According to the reference, these natural numbers can be listed as 1, 2, 3, 4, 5, 6, 7, 8 ... up to 100. Calculating the sum of this sequence of numbers results in 5050. This can be achieved through the use of a mathematical concept known as an arithmetic progression.
Here's a brief overview of how this sum is derived:
- Arithmetic Progression: A sequence of numbers where the difference between any two consecutive terms is constant. In this case, the common difference is 1.
- Formula for the Sum: There's a known formula for the sum of an arithmetic progression, which can be used to calculate the result directly. While not explicitly stated, the formula is: S = (n/2) * (a + l), where 'S' is the sum, 'n' is the number of terms, 'a' is the first term and 'l' is the last term.
- Application: In our case, n = 100, a = 1 and l= 100. Plugging these values into the formula, we get: S = (100/2) * (1+100) = 50 * 101 = 5050
Therefore, the answer 5050 is provided by the reference.
